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Simultaneously recorded electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI) is rapidly emerging as a powerful neurophysiological research and clinical tool. However, the quality of the EEG, recorded in the MRI scanner, is affected by the ballistocardiogram (BCG), which is an artifact related to the cardiac cycle. The BCG has a complete spectral overlap with the EEG and is nonstationary over time, making its suppression a signal processing challenge. We propose a novel method for the identification and suppression of this artifact using shape basis functions of the new dilated discrete Hermite transform. The BCG artifacts are modeled continuously, using these discrete Hermite basis functions and are subsequently subtracted from the ongoing EEG. Experimental EEG data was recorded within and outside a 3 Tesla MRI scanner, from a total of 6 subjects under a variety of experimental conditions. The efficiency of this algorithm was quantitatively assessed by adding known BCG templates, at varying Signal to Noise Ratios (SNRs), to EEG recorded outside the scanner. Significant suppression of the BCG artifact (p<0.05) was achieved without distorting the underlying EEG. Using EEG data recorded inside the MR scanner, this method was compared with existing BCG artifact removal techniques and its performance was found to be superior to the Average Artifact Subtraction (AAS) method and comparable to the Independent Component Analysis (ICA) based methods. The computational simplicity of this technique allows for real time implementation.